Search results for "STATISTICS & PROBABILITY"
showing 10 items of 436 documents
On BLD-mappings with small distortion
2021
We show that every $$L$$ -BLD-mapping in a domain of $$\mathbb {R}^{n}$$ is a local homeomorphism if $$L < \sqrt{2}$$ or $$K_I(f) < 2$$ . These bounds are sharp as shown by a winding map.
SOME RELATIONS BETWEEN BOUNDED BELOW ELLIPTIC OPERATORS AND STOCHASTIC ANALYSIS
2019
International audience; We apply Malliavin Calculus tools to the case of a bounded below elliptic rightinvariant Pseudodifferential operators on a Lie group. We give examples of bounded below pseudodifferential elliptic operators on R d by using the theory of Poisson process and the Garding inequality. In the two cases, there is no stochastic processes besides because the considered semi-groups do not preserve positivity.
Trace Operators on Regular Trees
2020
Abstract We consider different notions of boundary traces for functions in Sobolev spaces defined on regular trees and show that the almost everywhere existence of these traces is independent of the chosen definition of a trace.
Quasi-Continuous Vector Fields on RCD Spaces
2021
In the existing language for tensor calculus on RCD spaces, tensor fields are only defined $\mathfrak {m}$ -a.e.. In this paper we introduce the concept of tensor field defined ‘2-capacity-a.e.’ and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative.
Analysis of random walks on a hexagonal lattice
2019
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.
Inequalities for Information Potentials and Entropies
2020
We consider a probability distribution p0(x),p1(x),&hellip
Generalized Entropies, Variance and Applications
2020
The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the non-homogeneous Poisson process. We also get new expressions, bounds and stochastic comparisons involving such measures. Moreover, the dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions. In this framework we achieve some findings of interest in reliability theory, such as a characterization for the exponential distribution, various resul…
Selection bias was reduced by recontacting nonparticipants
2016
Objective One of the main goals of health examination surveys is to provide unbiased estimates of health indicators at the population level. We demonstrate how multiple imputation methods may help to reduce the selection bias if partial data on some nonparticipants are collected. Study Design and Setting In the FINRISK 2007 study, a population-based health study conducted in Finland, a random sample of 10,000 men and women aged 25–74 years were invited to participate. The study included a questionnaire data collection and a health examination. A total of 6,255 individuals participated in the study. Out of 3,745 nonparticipants, 473 returned a simplified questionnaire after a recontact. Both…
Planning and Analysis of Trials Using a Stepped Wedge Design: Part 26 of a Series on Evaluation of Scientific Publications
2019
Background The stepped-wedge design (SWD) of clinical trials has become very popular in recent years, particularly in health services research. Typically, study participants are randomly allotted in clusters to the different treatment options. Methods The basic principles of the stepped wedge design and related statistical techniques are described here on the basis of pertinent publications retrieved by a selective search in PubMed and in the CIS statistical literature database. Results In a typical SWD trial, the intervention is begun at a time point that varies from cluster to cluster. Until this time point is reached, all participants in the cluster belong to the control arm of the trial…
Cluster-Randomized Studies.
2018
Background Cluster-randomized trials (CRT) are needed to compare interventions that are allocated to entire groups of subjects, rather than to individuals. Publications about CRT have become steadily more common over the past decade. Readers of such publications should be able to categorize and interpret the findings of CRT correctly while considering the methodological requirements applicable to this type of study. Methods This review is based on a selection of pertinent literature and on the authors' expertise. CRT-specific methodological aspects of the planning, performance, and interpretation of studies are discussed. Results Readers of publications on CRT should check whether due consi…